Part A. For this part, we use two equations for linear motion:
y = y0 + v0 t + 0.5 g t^2 ---> 1
vf = v0 + g t ---> 2
First we solve for t using equation 1: y0 = 0 (initial point at top), y = 250 m, v0 = 0 (at rest)
250 = 0.5 (9.8) t^2
t = 7.143 s
Now we solve for final velocity vf using equation 2:
vf = g t
vf = 9.8 (7.143)
vf = 70 m/s
Part B. First we solve for the time it takes for the sound to reach the tourist.
t(sound) = 250 / 335 = 0.746 s
Therefore the total time would be:
t = 0.746 s + 0.300 s
t = 1.05 s
Hence there is enough time for the tourist to get out before the boulder hits him.
(a) It will strike the ground in 7.14 seconds
(b) The tourist at the bottom must get out in 6.10 seconds
Acceleration is rate of change of velocity.
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Let us now tackle the problem !
Given:
h = 250 m
Unknown:
t₁ = ?
t₂ = ?
Solution:
We can use the following formula to calculate time taken for the rock to reach the ground,
[tex]h = v ~ t + \frac{1}{2} ~ g ~ t^2[/tex]
[tex]250 = 0 \times t + \frac{1}{2} \times 9.8 ~ t^2[/tex]
[tex]250 = \frac{1}{2} \times 9.8 ~ t^2[/tex]
[tex]250 = 4.9 ~ t^2[/tex]
[tex]t^2 = 250 \div 4.9[/tex]
[tex]t = \sqrt{250 \div 4.9}[/tex]
[tex]t = \frac{50}{7} ~ seconds[/tex]
[tex]\large {\boxed {t \approx 7.14 ~ seconds} }[/tex]
Firstly, we will find the time taken by sound to reach the tourist.
[tex]t_{sound} = \frac{250 ~ m}{335 ~ m/s}[/tex]
[tex]\boxed{ t_{sound} = \frac{50}{67} ~ s }[/tex]
Next, we will find how long will a tourist have to get out of the way.
[tex]t_2 = t_1 - ( t_{sound} + t_{reaction})[/tex]
[tex]t_2 = \frac{50}{7} - ( \frac{50}{67} + 0.300})[/tex]
[tex]\large {\boxed {t_2 \approx 6.10 ~ seconds} }[/tex]
The tourist only has about 6 seconds before getting hit by the stone.
Grade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate
